Fernandez has already made two rehab starts at Class A Advanced Jupiter, but Miami is now advancing him to around 75-80 pitches in his upcoming start for the Zephyrs.

Along with Fernandez, Jarred Cosart will also make a rehab start this week for New Orleans. Cosart is lined up to start on Tuesday at Round Rock, which is expected to be his final outing before rejoining the Marlins.

Fernandez, recovering from Tommy John surgery, remains on schedule to join Miami around July 1-7.

Cosart, on the disabled list with vertigo, has not started for the Marlins since May 13. The right-hander is 1-3 with a 4.08 ERA in seven starts. This will be Cosart's second start for New Orleans. He gave up two runs on nine hits in 5 2/3 innings on Thursday.

After getting through Tuesday, Cosart is expected to mix back into Miami's rotation. Exactly where remains to be determined.

The Marlins are staying with their current rotation, with Tom Koehler set to face the Yankees on Monday and David Phelps on Tuesday at Marlins Park.

"The next change will be when Cosart comes back," manager Dan Jennings said. "Then we'll go from there."

In Fernandez's first two rehab starts, he's had mixed results. He had to battle in his first game, giving up five runs in three innings. But on Thursday, facing Port Charlotte for the second time, Fernandez impressed in five shutout innings, allowing two hits with four strikeouts.

"After this last one, he was on cloud nine, he was so excited," Jennings said.

In the second start, the ace threw more breaking balls than the first outing.

First baseman Michael Morse, on the DL since May 26 with a right ring finger sprain, is swinging the bat better. He could be playing in rehab games at Jupiter as early as Wednesday.

"It's coming around," Jennings said. "I think now he is actually swinging the bat without pain in the joint."